The solution of the system of linear equations is (x, y, z) = (1, - 1, 2).
Herein we have a system of three linear equations with three variables, whose matricial form is shown below:
[tex]\left[\begin{array}{ccc}1&5&- 3\\- 5&6&- 5\\- 1&8&- 8\end{array}\right] \cdot \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}- 10\\- 21\\- 25\end{array}\right][/tex]
Based on linear algebra, the solution of the system is:
X = A⁻¹ · B (1)
Where:
And the inverse of the matrix A is equal to:
A⁻¹ = adj (A) / det (A) (2)
Where:
By linear algebra, we find that the inverse of the matrix A is:
[tex]adj (\vec A) = \left[\begin{array}{ccc}8&- 16&7\\35&11&- 20\\34&13&- 31\end{array}\right][/tex]
det (A) = 81
[tex]\vec A ^{-1} = \left[\begin{array}{ccc}\frac{8}{81} &-\frac{16}{81} &\frac{7}{81} \\\frac{35}{81} &\frac{11}{81} &-\frac{20}{81} \\\frac{34}{81} &\frac{13}{81} &- \frac{31}{81} \end{array}\right][/tex]
Now we find the solution of the system of linear equations:
[tex]\vec X = \left[\begin{array}{ccc}\frac{8}{81} &-\frac{16}{81} &\frac{7}{81} \\\frac{35}{81} &\frac{11}{81} &-\frac{20}{81} \\\frac{34}{81} &\frac{13}{81} &- \frac{31}{81} \end{array}\right] \cdot \left[\begin{array}{ccc}-10&\\-21\\-25\end{array}\right][/tex]
[tex]\vec X = \left[\begin{array}{ccc}1\\- 1\\2\end{array}\right][/tex]
The solution of the system of linear equations is (x, y, z) = (1, - 1, 2).
The statement presents typing mistakes. Correct form is shown below:
Use an inverse matrix to solve the system of equation if possible:
x + 5 · y - 3 · z = - 10
- 5 · x + 6 · y - 5 · z = - 21
- x + 8 · y - 8 · z = - 25
To learn more on systems of linear equations: https://brainly.com/question/20379472
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